Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{9} - 63x^{7} + 1323x^{5} - 10290x^{3} + 21609x - 5831 \)
| $\times$ | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 184, ·)\) | \(\chi_{ 189 } ( 25, ·)\) | \(\chi_{ 189 } ( 151, ·)\) | \(\chi_{ 189 } ( 88, ·)\) | \(\chi_{ 189 } ( 121, ·)\) | \(\chi_{ 189 } ( 58, ·)\) | \(\chi_{ 189 } ( 127, ·)\) |
|---|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 189 }(1, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 184, ·)\) | \(\chi_{ 189 } ( 25, ·)\) | \(\chi_{ 189 } ( 151, ·)\) | \(\chi_{ 189 } ( 88, ·)\) | \(\chi_{ 189 } ( 121, ·)\) | \(\chi_{ 189 } ( 58, ·)\) | \(\chi_{ 189 } ( 127, ·)\) |
| \(\chi_{ 189 }(64, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 58, ·)\) | \(\chi_{ 189 } ( 88, ·)\) | \(\chi_{ 189 } ( 25, ·)\) | \(\chi_{ 189 } ( 151, ·)\) | \(\chi_{ 189 } ( 184, ·)\) | \(\chi_{ 189 } ( 121, ·)\) | \(\chi_{ 189 } ( 1, ·)\) |
| \(\chi_{ 189 }(184, ·)\) | \(\chi_{ 189 } ( 184, ·)\) | \(\chi_{ 189 } ( 58, ·)\) | \(\chi_{ 189 } ( 25, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 151, ·)\) | \(\chi_{ 189 } ( 88, ·)\) | \(\chi_{ 189 } ( 121, ·)\) |
| \(\chi_{ 189 }(25, ·)\) | \(\chi_{ 189 } ( 25, ·)\) | \(\chi_{ 189 } ( 88, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 58, ·)\) | \(\chi_{ 189 } ( 184, ·)\) | \(\chi_{ 189 } ( 121, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 151, ·)\) |
| \(\chi_{ 189 }(151, ·)\) | \(\chi_{ 189 } ( 151, ·)\) | \(\chi_{ 189 } ( 25, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 184, ·)\) | \(\chi_{ 189 } ( 121, ·)\) | \(\chi_{ 189 } ( 58, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 88, ·)\) |
| \(\chi_{ 189 }(88, ·)\) | \(\chi_{ 189 } ( 88, ·)\) | \(\chi_{ 189 } ( 151, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 121, ·)\) | \(\chi_{ 189 } ( 58, ·)\) | \(\chi_{ 189 } ( 184, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 25, ·)\) |
| \(\chi_{ 189 }(121, ·)\) | \(\chi_{ 189 } ( 121, ·)\) | \(\chi_{ 189 } ( 184, ·)\) | \(\chi_{ 189 } ( 151, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 88, ·)\) | \(\chi_{ 189 } ( 25, ·)\) | \(\chi_{ 189 } ( 58, ·)\) |
| \(\chi_{ 189 }(58, ·)\) | \(\chi_{ 189 } ( 58, ·)\) | \(\chi_{ 189 } ( 121, ·)\) | \(\chi_{ 189 } ( 88, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 64, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 25, ·)\) | \(\chi_{ 189 } ( 151, ·)\) | \(\chi_{ 189 } ( 184, ·)\) |
| \(\chi_{ 189 }(127, ·)\) | \(\chi_{ 189 } ( 127, ·)\) | \(\chi_{ 189 } ( 1, ·)\) | \(\chi_{ 189 } ( 121, ·)\) | \(\chi_{ 189 } ( 151, ·)\) | \(\chi_{ 189 } ( 88, ·)\) | \(\chi_{ 189 } ( 25, ·)\) | \(\chi_{ 189 } ( 58, ·)\) | \(\chi_{ 189 } ( 184, ·)\) | \(\chi_{ 189 } ( 64, ·)\) |